A path consists of two consecutive parametric segments: Segment I:

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

x(t)=t,\;y(t)=0,\;0\le t\le 3

. Segment II:

x(\theta)=3+2\cos\theta,\;y(\theta)=2\sin\theta,\;0\le \theta\le\dfrac{\pi}{2}

. Determine the total length of the complete path. (a)

3+\dfrac{\pi}{2}

(b)

2\pi

(c)

3+\pi

(d)

3+2\pi